Why does a child in a wagon seem tozdagf:m 2c ui-a*qmds 69 +h9c fall backward when you give the wagon a sharp p s add imu 9hcqgm6-*a:cfz29+ull forward?

A box rests on the (frictionlel*(i nsqh7-xxin7::fglb x k 8ss) bed of a truck. The truck driver starts the truck*fh xi qlxkg ::n-is7x( b8nl7 and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? l -6)gusczcd./ *iuj fExplain.

Only one force acts on an object. Can the object have zero acceleration? C7x fe*dei n448ka7:nluw-,d4f gtka yan it have di8 n4w:et, xk7ank*fa lf 4ygd4e7-u zero velocity? Explain.

When a golf ball is dropped to the pavement, it bo-s2yz3,lr fcvunces back up. (a) Is a force needed to make it bounce back up?- 3,s2lrfcvz y (b) If so, what exerts the force?

If you walk along a log floa/ egyzy0l7;r rb/m 3rsting on a lake, why does the log move in the opposite directiy/y br 0sgl3re rm/;7zon?

Why might your foot hurt if you kick a heavy dese nu-d1oa (3q1;iyy9yz nr*f hk or a wall?

  When you are running and want to stop quickly, you mustjh7fnfs4rf7,fqk 4ukbp i +;. decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to comejqs;,4frfu 7 k.7n+ 4kffibph to rest.    m/s$^2$

A stone hangs by a fine thread from the;wjrrox; h*jz1fb /un7n9 2tn ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a1h zw7n rxfn9jr/b ;*u;2oj nt sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg roy8e6:pg)4p ccspp yok hc7- 3ock is twice as great as that on a 1-kg rock. Why then doesn’to-og y pc7 c)yespk4p83 c6:ph the heavier rock fall faster?

Would a spring scale carried to the Moon give accura1+*msxh tvuaq2s:h .t te results if the scale had been calibrated (h *xq 1s2s:aumt.+vhta) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless t5tkd hmcw j o1y9c,0, bfre1z7zblm53t9sz4uable using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase9 csz3,19m 1 e75chob udwzbrz,tjk054yl mft, or (c) decrease? Explain.

When an object falls freely under the influevajw* u:d:9d8fjesq 0nce of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerdj9sv*u8je afw qd0:: ts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are op o .orowx(5x)n the Moon with the force needed to lift it on rwp o).5( ooxxEarth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls c,xp6f/dibyxf))9 irwf w 75twith equal force on the other team. What, then, d5 wxy)d7p9b)iix,wr/ff t6fcetermines which team will win?

A person exerts an upward force of 40 N tdctob o21 ,6wzo hold a bag of groceries. Describe the “reaction” force (Newton’s t,1 6dz2bt cwoohird law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still f9y yem v6+bqlloa62-on the ground, how large a force does the ground exert on you? Why doesn’t this force make eo yvl29fl -6yq6mb a+you rise up into the air?

Whiplash sometimes results from an auzi uow,r o/aa)p 9v7/htomobile accident when the victim’s car is struck violently from the rear. Explava)z opu/w7a/or 9,ihin why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. xx20by9p / q2v(jdpi xWhen the truck accelerates, the crate remains xj 0vyqpxb9 / 2(pdxi2where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block r,xs rw4t-z9b/ vhyln;;;mup o *re 7gxeaches its highest point, it slides back down but the magnitude of its acceleration is less on therxpls em;4;o -z w*;bg,rvx7ty /n 9hu descent than on the ascent. Why?

What would your bathroom scale read if you weighed wa*j 4yez qd 29u7ldu1yourself on an inclined plane? Assume the mecha 9d*uqe4j71 dza2ywlunism functions properly, even at an angle.

  What force is needed to acceler3,y a0dkcug 2u+ ytd/i9f*jjlv 1 8tuhate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acce, nkott b;k2 h)(u/wwp ++whvblerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate kh(* gf,q g qfzm9xl58a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of*ev:ra14v*zmaso o7a tf;rgv 4dxu*) a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.ty; uuhjtnbl, j6+(z30 s if the car is trajhnu ut t ;b6,lz+(y3jveling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125mir 283xnf7b fw/s over a distanbff78rw x2 3ince of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the waterq((7dy 1k a-uhxkiny, do9o (t with an acceleration of 2.5y1ak,dq-h 7 x(i(y(on9t do ku $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a w.t ziwx .lhf/8kstmz0.2bv; quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be dt hci v.8o;r,otr6ag60po(qux ac fgl0 : *,tjesigned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert o:a o,ur,8*. 6pfvqx;h gto 0ajlt0c irc(6gt on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. When the elevatjm19:m4v.wx a4q t kmbor begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and f4qjb9tm14wa.:v mkxm ind the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg eu x,; kj*lko q/km*k*zlevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator wiz kj /lo;x*qkm*k, *ukthout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling skyoe j vwtdyi+:z2-ifpvt0t( wp56,l f- divers (mass 132 kg including parachute) when-t 5dt:,ypjt zw(ivio 20+v ef6w fp-l the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof 9n m/j9s m8,:nkwovgiof a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approvnnki:98 9o,mmw gs j/ximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a tadnt4;3d8x xatlmf4b0rcq7o0 ble. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hantdr 0x ;n7 fcx0d8m3l4t bo4aqging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basky 9vq+(pyzt:2ll a7xcetball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a); h:q0 smruy-s at the moment it is hit by the bat, and a;q0hm-y: ssurgain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly dik d91ai3f c* 5ybi.jjxrection. A second 650-N force must be exerted in what direction so that the resultant of the two forcesfi9k3bj x1*djcia 5y. points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acr4htj1 aev) 2hsoss a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she1)4v tjhh2esa is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cor6c :tu8mt bn)rd from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.p rqzwup q.ca 113/ns-0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unity rty 8x d.n6x2iq1 d,cszfbi ole,k7zj2-e-7 to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of2jdd ,x.18inl,qb7--6yzoeitexs k 7c zyfr2 the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of thcfxjh;vh 0*1i;jdlx 2e same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling betweeh;v1 lc jxxidj*20h ;fn the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus shown a(7w4um7 g 3wya8oli l6p ;4awhqhro7in Fig. 4-48. (7l i78rh6p4w ; 4 3qygawuaowoham7 (la) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a rac6niyewa ; nsh ))) +5zz sv7nhghxtge;fu8*7 ie began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a gb1tt0dg748hno 4k gb block (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a fr;l s*0e2d:(zrosus6 g/lu7 ifybswlj4/4f z yictionless horizontal surface are in contact with each other, as sdlu s/ 0ryoj;sl6b/*zw2gz( s4l f47i f:ys uehown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m eum9oyhcvq zvbpp; ,s l10*45 above the ground, and the maz, lob1qpuc*;pe4v mv5hs90 y ssless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionles p(5kwqufiam y4 pc/w.6ro) y3s table are connected by a heavy cord of mass 1.0 kg . Calculate th c( qwy.345wor /fym)k6ipupae acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic bbrv)g0g 7t i9friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is requir*z7rpi9 49. tvrrjyl 4e; zbl,elvgsk n 7:jt8ed to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accepyr ()xq,lk*e6bptys. m72 atlerating at 0.20g. What minimum coefficient of static friction must exist betw(s)t 2 b *,.teyxrq6klymapp7een your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car 4ym/njy jyhmud:6 u*:can undergo if the coefficient of static friction between the tires and thejy4 h/ y6mn:juuy:*dm ground is 0.80?   

  The coefficient of static friction between hard rubber and norm2 p1an vhu ile9j2ov+7+0gt igal street pavement is about 0.8. On how steep a hill (maximum angle) can9 o vlghtv+1ni7paj e2+u2g0i you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.80f1 4:d nc2mhue $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rou2dbtm ;c +khq6gh 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have o qcetr8:*1 -d uh6p97v irhrna very high coefficient e1rqi- nr hp*6tor ucdv:7 h98of static friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction fou0 q, i2heua7ar a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Exampl*7ef 6omvwtk2 :z,kgde 4-20) how large a mass would box A have to have to prevent any motion from : o veg26m7f ,dk*twzkoccurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will syp mo/op v-3+ (xkvl559g thkit go, given that the coefficivy ml -x9t+ov pp5kh53gos(k/ent of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg p /r7ujv,e:sj t8o 2eaand 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). j,ue/roap e2v8 7:stj A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heak:c*3fr7mp drqjdmc5 1z9.ice p yu--vy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelem3.cd zpcu:95 c r*-peqyd7fm 1jir- krate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about 3hw*+wegrc, lrn*9v rparking your car in your driveway, which has an incline of lrve9+ cr,w* 3*rwhgn 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a svjteoy 6j j) 4m; 6*wwv3z:ejelide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-ld-khqp )) jj-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed ofkz*2c lu, agfgf58lp-y1g sl6 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top a35 s9hs8n2db( mzn6lb qa1u oof the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place again.fz ka,xgl f(e r/x+4+t lpup)st a rough wall by someone pushing on it with a force r.ulxlf(fgp4x k)+ ,/atz+epdirected upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roy 1css k*gmn;hw+r 8nl7l /jx:y) :eakofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge l1xh*krc/ 8;n lwek:gyssy+:7jam n)of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile travelin e, 8*v.sdody-fc5 vlqg at speed v i, 8dfed lsqv.o5*cy-v s equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard 0w)ekzfw * v0hyl-fbh, i1 cz*of a car slides forward on the dash when the driver decelerates eivh-wzk f y0*hf1l *,bzc 0)wfrom 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial t vybg,n,p3a*ts)q;iae ar2o ;y23if speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a convey bjc6 x8s)xj6 n:rdf0aor belt from where they are filled to the packing stat:jd cj6b8)0xfrs x6an ion 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kineti/)u9nxi2xb f rc friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the b 1vbb +d00r1)etttfp sicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian he;rch9zzrphp yo r/(9s+yh caw(+.wq0art, at each pulse approximately 20 g of blood is accelerated from 09(+w qrrch0azc/p.yz9 r;+hsp (owyh.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of survhmtwj2 so)z 9ojn p1:4iving an automobile crash if the deceleration is no more than 30 " 4ztjpwn jo2m:) 1h s9og 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake 8iga js:r2pg :is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground g 2rijp :g8:asmust be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the -/pnmfn .f vd-scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coef fv/n. df--npmficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-4 tr1::sr upera k6-ccin-4 means that for each 4 m traveled along the road, the e1 a:tkc surr 4r:6cep-levation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and fallsys md) s;:i,yf 55 m bes);ids ym ,fy:fore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy str -t.ta ermq;he 8.l;sletch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon em.m lt. ; ;seqe-atlrh8erging?   

  A city planner is working on the redesign of a hilly portioe4 l( ;94tlxofly3 ocxn of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg le4 of ;c4 xl(oxtyl93, can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physicsx*d ayongel th y,/5/qs+i 2h) experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off /s*xh/ylqiy nat,)ogh5 2+ed from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be ui7f,ogf3igaf32 swbc a92y+several ramps connecting different parts of 3fai2,f o9b a3wgf2s+7iucg y the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) usj)3cdps0w8au 0)f ob ding the pulley apparat 3pd)fa00 sdb8o w)cjuus shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at 3.+ w 0dc(5t;owjed *yst5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-resh6y . /ag/xkuvtraint chair, an engineer considers the following set of conditions: 6.g/ xk/ahu vy
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metric ton2m,neys-* ut;a hj *0 djpr,zms (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of simi:qj: 6xzhph0ay jsx 1;wv2- xcd,nrv9lar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a hx-ysa20 :vvjjx,wxq r16 9n;h cpd:zstatic rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a "mdrwqlk*l6g3dz:a71 3swbb jaw d* /8 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building isi lo+ xx-zm2 w2b,3vt,swg*o l allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are a)5xxv niycgu7d j 0/x,scending an ice field inclined at x/)0,5ny7xv i jxudcg 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.